/* ----------------------------------------------------------------------  
* Copyright (C) 2010 ARM Limited. All rights reserved.  
*  
* $Date:        29. November 2010  
* $Revision: 	V1.0.3  
*  
* Project: 	    CMSIS DSP Library  
* Title:	    arm_dct4_f32.c  
*  
* Description:	Processing function of DCT4 & IDCT4 F32.  
*  
* Target Processor: Cortex-M4/Cortex-M3
*  
* Version 1.0.3 2010/11/29 
*    Re-organized the CMSIS folders and updated documentation.  
*   
* Version 1.0.2 2010/11/11  
*    Documentation updated.   
*  
* Version 1.0.1 2010/10/05   
*    Production release and review comments incorporated.  
*  
* Version 1.0.0 2010/09/20   
*    Production release and review comments incorporated.  
* -------------------------------------------------------------------- */ 
 
#include "arm_math.h" 
 
/**  
 * @ingroup groupTransforms  
 */ 
 
/**  
 * @defgroup DCT4_IDCT4 DCT Type IV Functions  
 * Representation of signals by minimum number of values is important for storage and transmission.  
 * The possibility of large discontinuity between the beginning and end of a period of a signal  
 * in DFT can be avoided by extending the signal so that it is even-symmetric.  
 * Discrete Cosine Transform (DCT) is constructed such that its energy is heavily concentrated in the lower part of the  
 * spectrum and is very widely used in signal and image coding applications.  
 * The family of DCTs (DCT type- 1,2,3,4) is the outcome of different combinations of homogeneous boundary conditions.  
 * DCT has an excellent energy-packing capability, hence has many applications and in data compression in particular.  
 *  
 * DCT is essentially the Discrete Fourier Transform(DFT) of an even-extended real signal.  
 * Reordering of the input data makes the computation of DCT just a problem of  
 * computing the DFT of a real signal with a few additional operations.  
 * This approach provides regular, simple, and very efficient DCT algorithms for practical hardware and software implementations.  
 *   
 * DCT type-II can be implemented using Fast fourier transform (FFT) internally, as the transform is applied on real values, Real FFT can be used.  
 * DCT4 is implemented using DCT2 as their implementations are similar except with some added pre-processing and post-processing.  
 * DCT2 implementation can be described in the following steps:  
 * - Re-ordering input  
 * - Calculating Real FFT  
 * - Multiplication of weights and Real FFT output and getting real part from the product.  
 *  
 * This process is explained by the block diagram below:  
 * \image html DCT4.gif "Discrete Cosine Transform - type-IV"  
 *  
 * \par Algorithm:  
 * The N-point type-IV DCT is defined as a real, linear transformation by the formula:  
 * \image html DCT4Equation.gif  
 * where <code>k = 0,1,2,.....N-1</code>  
 *\par  
 * Its inverse is defined as follows:  
 * \image html IDCT4Equation.gif  
 * where <code>n = 0,1,2,.....N-1</code>  
 *\par  
 * The DCT4 matrices become involutory (i.e. they are self-inverse) by multiplying with an overall scale factor of sqrt(2/N).  
 * The symmetry of the transform matrix indicates that the fast algorithms for the forward  
 * and inverse transform computation are identical.  
 * Note that the implementation of Inverse DCT4 and DCT4 is same, hence same process function can be used for both.  
 *  
 * \par Lengths supported by the transform:  
 *  As DCT4 internally uses Real FFT, it supports all the lengths supported by arm_rfft_f32().  
 * The library provides separate functions for Q15, Q31, and floating-point data types.  
 * \par Instance Structure  
 * The instances for Real FFT and FFT, cosine values table and twiddle factor table are stored in an instance data structure.  
 * A separate instance structure must be defined for each transform.  
 * There are separate instance structure declarations for each of the 3 supported data types.  
 *  
 * \par Initialization Functions  
 * There is also an associated initialization function for each data type.  
 * The initialization function performs the following operations:  
 * - Sets the values of the internal structure fields.  
 * - Initializes Real FFT as its process function is used internally in DCT4, by calling arm_rfft_init_f32().  
 * \par  
 * Use of the initialization function is optional.  
 * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.  
 * To place an instance structure into a const data section, the instance structure must be manually initialized.  
 * Manually initialize the instance structure as follows:  
 * <pre>  
 *arm_dct4_instance_f32 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft};  
 *arm_dct4_instance_q31 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; 
 *arm_dct4_instance_q15 S = {N, Nby2, normalize, pTwiddle, pCosFactor, pRfft, pCfft}; 
 * </pre> 
 * where \c N is the length of the DCT4; \c Nby2 is half of the length of the DCT4; 
 * \c normalize is normalizing factor used and is equal to <code>sqrt(2/N)</code>;  
 * \c pTwiddle points to the twiddle factor table; 
 * \c pCosFactor points to the cosFactor table; 
 * \c pRfft points to the real FFT instance; 
 * \c pCfft points to the complex FFT instance; 
 * The CFFT and RFFT structures also needs to be initialized, refer to arm_cfft_radix4_f32() 
 * and arm_rfft_f32() respectively for details regarding static initialization. 
 * 
 * \par Fixed-Point Behavior  
 * Care must be taken when using the fixed-point versions of the DCT4 transform functions.  
 * In particular, the overflow and saturation behavior of the accumulator used in each function must be considered.  
 * Refer to the function specific documentation below for usage guidelines.  
 */ 
 
 /**  
 * @addtogroup DCT4_IDCT4  
 * @{  
 */ 
 
/**  
 * @brief Processing function for the floating-point DCT4/IDCT4. 
 * @param[in]       *S             points to an instance of the floating-point DCT4/IDCT4 structure. 
 * @param[in]       *pState        points to state buffer. 
 * @param[in,out]   *pInlineBuffer points to the in-place input and output buffer. 
 * @return none. 
 */ 
 
void arm_dct4_f32( 
  const arm_dct4_instance_f32 * S, 
  float32_t * pState, 
  float32_t * pInlineBuffer) 
{ 
  uint32_t i;                                    /* Loop counter */ 
  float32_t *weights = S->pTwiddle;              /* Pointer to the Weights table */ 
  float32_t *cosFact = S->pCosFactor;            /* Pointer to the cos factors table */ 
  float32_t *pS1, *pS2, *pbuff;                  /* Temporary pointers for input buffer and pState buffer */ 
  float32_t in;                                  /* Temporary variable */ 
 
 
  /* DCT4 computation involves DCT2 (which is calculated using RFFT)  
   * along with some pre-processing and post-processing.  
   * Computational procedure is explained as follows:  
   * (a) Pre-processing involves multiplying input with cos factor,  
   *     r(n) = 2 * u(n) * cos(pi*(2*n+1)/(4*n))  
   *              where,  
   *                 r(n) -- output of preprocessing  
   *                 u(n) -- input to preprocessing(actual Source buffer)  
   * (b) Calculation of DCT2 using FFT is divided into three steps:  
   *                  Step1: Re-ordering of even and odd elements of input.  
   *                  Step2: Calculating FFT of the re-ordered input.  
   *                  Step3: Taking the real part of the product of FFT output and weights.  
   * (c) Post-processing - DCT4 can be obtained from DCT2 output using the following equation:  
   *                   Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)  
   *                        where,  
   *                           Y4 -- DCT4 output,   Y2 -- DCT2 output  
   * (d) Multiplying the output with the normalizing factor sqrt(2/N).  
   */ 
 
        /*-------- Pre-processing ------------*/ 
  /* Multiplying input with cos factor i.e. r(n) = 2 * x(n) * cos(pi*(2*n+1)/(4*n)) */ 
  arm_scale_f32(pInlineBuffer, 2.0f, pInlineBuffer, S->N); 
  arm_mult_f32(pInlineBuffer, cosFact, pInlineBuffer, S->N); 
 
  /* ----------------------------------------------------------------  
   * Step1: Re-ordering of even and odd elements as,  
   *             pState[i] =  pInlineBuffer[2*i] and  
   *             pState[N-i-1] = pInlineBuffer[2*i+1] where i = 0 to N/2  
   ---------------------------------------------------------------------*/ 
 
  /* pS1 initialized to pState */ 
  pS1 = pState; 
 
  /* pS2 initialized to pState+N-1, so that it points to the end of the state buffer */ 
  pS2 = pState + (S->N - 1u); 
 
  /* pbuff initialized to input buffer */ 
  pbuff = pInlineBuffer; 
 
  /* Initializing the loop counter to N/2 >> 2 for loop unrolling by 4 */ 
  i = (uint32_t) S->Nby2 >> 2u; 
 
  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
   ** a second loop below computes the remaining 1 to 3 samples. */ 
  do 
  { 
    /* Re-ordering of even and odd elements */ 
    /* pState[i] =  pInlineBuffer[2*i] */ 
    *pS1++ = *pbuff++; 
    /* pState[N-i-1] = pInlineBuffer[2*i+1] */ 
    *pS2-- = *pbuff++; 
 
    *pS1++ = *pbuff++; 
    *pS2-- = *pbuff++; 
 
    *pS1++ = *pbuff++; 
    *pS2-- = *pbuff++; 
 
    *pS1++ = *pbuff++; 
    *pS2-- = *pbuff++; 
 
    /* Decrement the loop counter */ 
    i--; 
  } while(i > 0u); 
 
  /* pbuff initialized to input buffer */ 
  pbuff = pInlineBuffer; 
 
  /* pS1 initialized to pState */ 
  pS1 = pState; 
 
  /* Initializing the loop counter to N/4 instead of N for loop unrolling */ 
  i = (uint32_t) S->N >> 2u; 
 
  /* Processing with loop unrolling 4 times as N is always multiple of 4.  
   * Compute 4 outputs at a time */ 
  do 
  { 
    /* Writing the re-ordered output back to inplace input buffer */ 
    *pbuff++ = *pS1++; 
    *pbuff++ = *pS1++; 
    *pbuff++ = *pS1++; 
    *pbuff++ = *pS1++; 
 
    /* Decrement the loop counter */ 
    i--; 
  } while(i > 0u); 
 
 
  /* ---------------------------------------------------------  
   *     Step2: Calculate RFFT for N-point input  
   * ---------------------------------------------------------- */ 
  /* pInlineBuffer is real input of length N , pState is the complex output of length 2N */ 
  arm_rfft_f32(S->pRfft, pInlineBuffer, pState); 
 
        /*----------------------------------------------------------------------  
	 *  Step3: Multiply the FFT output with the weights.  
	 *----------------------------------------------------------------------*/ 
  arm_cmplx_mult_cmplx_f32(pState, weights, pState, S->N); 
 
  /* ----------- Post-processing ---------- */ 
  /* DCT-IV can be obtained from DCT-II by the equation,  
   *       Y4(k) = Y2(k) - Y4(k-1) and Y4(-1) = Y4(0)  
   *       Hence, Y4(0) = Y2(0)/2  */ 
  /* Getting only real part from the output and Converting to DCT-IV */ 
 
  /* Initializing the loop counter to N >> 2 for loop unrolling by 4 */ 
  i = ((uint32_t) S->N - 1u) >> 2u; 
 
  /* pbuff initialized to input buffer. */ 
  pbuff = pInlineBuffer; 
 
  /* pS1 initialized to pState */ 
  pS1 = pState; 
 
  /* Calculating Y4(0) from Y2(0) using Y4(0) = Y2(0)/2 */ 
  in = *pS1++ * (float32_t) 0.5; 
  /* input buffer acts as inplace, so output values are stored in the input itself. */ 
  *pbuff++ = in; 
 
  /* pState pointer is incremented twice as the real values are located alternatively in the array */ 
  pS1++; 
 
  /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.  
   ** a second loop below computes the remaining 1 to 3 samples. */ 
  do 
  { 
    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 
    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 
    in = *pS1++ - in; 
    *pbuff++ = in; 
    /* points to the next real value */ 
    pS1++; 
 
    in = *pS1++ - in; 
    *pbuff++ = in; 
    pS1++; 
 
    in = *pS1++ - in; 
    *pbuff++ = in; 
    pS1++; 
 
    in = *pS1++ - in; 
    *pbuff++ = in; 
    pS1++; 
 
    /* Decrement the loop counter */ 
    i--; 
  } while(i > 0u); 
 
  /* If the blockSize is not a multiple of 4, compute any remaining output samples here.  
   ** No loop unrolling is used. */ 
  i = ((uint32_t) S->N - 1u) % 0x4u; 
 
  while(i > 0u) 
  { 
    /* Calculating Y4(1) to Y4(N-1) from Y2 using equation Y4(k) = Y2(k) - Y4(k-1) */ 
    /* pState pointer (pS1) is incremented twice as the real values are located alternatively in the array */ 
    in = *pS1++ - in; 
    *pbuff++ = in; 
    /* points to the next real value */ 
    pS1++; 
 
    /* Decrement the loop counter */ 
    i--; 
  } 
 
 
        /*------------ Normalizing the output by multiplying with the normalizing factor ----------*/ 
 
  /* Initializing the loop counter to N/4 instead of N for loop unrolling */ 
  i = (uint32_t) S->N >> 2u; 
 
  /* pbuff initialized to the pInlineBuffer(now contains the output values) */ 
  pbuff = pInlineBuffer; 
 
  /* Processing with loop unrolling 4 times as N is always multiple of 4.  Compute 4 outputs at a time */ 
  do 
  { 
    /* Multiplying pInlineBuffer with the normalizing factor sqrt(2/N) */ 
    in = *pbuff; 
    *pbuff++ = in * S->normalize; 
 
    in = *pbuff; 
    *pbuff++ = in * S->normalize; 
 
    in = *pbuff; 
    *pbuff++ = in * S->normalize; 
 
    in = *pbuff; 
    *pbuff++ = in * S->normalize; 
 
    /* Decrement the loop counter */ 
    i--; 
  } while(i > 0u); 
 
} 
 
/**  
   * @} end of DCT4_IDCT4 group  
   */ 
